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This paper is to deal with the blind extraction problem of chaotic signals by using a linear mixing model. In this model, a novel method to describe the distance function in a high dimensional space is proposed which relates the kernel function to objective function. When adopting the artificial bee colony algorithm (ABCA) as an alternative method to solve a multi-modal optimization problem, its analysis under a Markov chain model is also presented. The simulation results show that the objective function of this article has low complexity, and the artificial bee colony algorithm converges to a local minimum quickly. To be specific, the target function is constructed by combining the advantages of the proliferation exponent and the distance kernel function. The proliferation exponent can reflect the chaotic properties of a signal to a large extent, and the distance kernel can help to describe the statistical properties in a higher dimension. Due to the fact that only one frame of time-delay embedded signal is adopted, the computational complexity of our target function is low. The artificial bee colony algorithm is shown to be advantageous over other swarm algorithms. Although adopting ABCA for our evaluation function seems easy, we analyze why this algorithm can work, in contrast to the fact that most literature only runs some simulations to confirm its usefulness. Our analysis is only for a special case when the number of employed bees is set to be 2 and the process of onlooker bees and scouts are temporarily omitted. With smaller complexity than the methods based on proliferation exponents and kurtosises, simulations show that our method can have excellent performance when evaluated by correlation coefficients.
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Keywords:
- chaotic signal /
- blind extraction /
- kernel function /
- artificial bee colony algorithm
[1] Feng J C 2012 Chaotic Signals and Information Processing (Beijing:Tsinghua Univ. Press) pp32-35(in Chinese)[冯久超2012混沌信号与信息处理(清华大学出版社)第32–35页]
[2] Hu Z H, Feng J C 2011 Acta Phys. Sin. 60 070505 (in Chinese)[胡志辉, 冯久超2011 60 070505]
[3] Hathaway D H, Wilson R M 2010 Sol. Phys. 224 5
[4] Letellier C, Aguirre L A, Maquet J, Gilmore R 2006 Astron. Astrophys. 449 379
[5] Mordvinov A V, Kramynin A P 2010 Sol. Phys. 264 269
[6] Li G M, Lyu S X 2015 Chin. J. Electron. 24 584
[7] Wang B Y, Zheng W X 2006 IEEE Trans. Circuits Syst. Express Briefs 53 143
[8] Arena P, Buscarino A, Fortuna L, Frasca M 2006 Phys. Rev. E 74 1
[9] Hu W, Liu Z 2008 IET Signal Proc. 2 424
[10] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[11] Barros A K, Cichocki A 2001 Neural Comput. 13 1995
[12] Ahmadian P, Sanei S, Ascari L, Villanueva L G, Umilta M A 2013 IEEE Trans. Neural Syst. Rehabil. Eng. 21 567
[13] Chen H B, Feng J C, Fang Y 2008 Chin. Phys. Lett. 25 405
[14] Li Y, Wang J, Zurada J M 2000 IEEE Trans. Neural Networks 11 1413
[15] L S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506
[16] Scholkopf B 2001 Adv. Neural Inf. Proc. Syst. 13 301
[17] Kwak N 2013 IEEE Trans. Neural Networks and Learning Systems 24 2113
[18] Karaboga D, Basturk B 2007 J. Global Optim. 39 459
[19] Karaboga D, Basturk B 2008 Appl. Soft Comput. J. 8 687
[20] Chen Y, L S X, Wang M J, Feng J C 2015 Acta Phys. Sin. 64 090501 (in Chinese)[陈越, 吕善翔, 王梦蛟, 冯久超2015 64 090501]
[21] Hyvarinen A, Oja E 2000 Neural Networks 13 411
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[1] Feng J C 2012 Chaotic Signals and Information Processing (Beijing:Tsinghua Univ. Press) pp32-35(in Chinese)[冯久超2012混沌信号与信息处理(清华大学出版社)第32–35页]
[2] Hu Z H, Feng J C 2011 Acta Phys. Sin. 60 070505 (in Chinese)[胡志辉, 冯久超2011 60 070505]
[3] Hathaway D H, Wilson R M 2010 Sol. Phys. 224 5
[4] Letellier C, Aguirre L A, Maquet J, Gilmore R 2006 Astron. Astrophys. 449 379
[5] Mordvinov A V, Kramynin A P 2010 Sol. Phys. 264 269
[6] Li G M, Lyu S X 2015 Chin. J. Electron. 24 584
[7] Wang B Y, Zheng W X 2006 IEEE Trans. Circuits Syst. Express Briefs 53 143
[8] Arena P, Buscarino A, Fortuna L, Frasca M 2006 Phys. Rev. E 74 1
[9] Hu W, Liu Z 2008 IET Signal Proc. 2 424
[10] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[11] Barros A K, Cichocki A 2001 Neural Comput. 13 1995
[12] Ahmadian P, Sanei S, Ascari L, Villanueva L G, Umilta M A 2013 IEEE Trans. Neural Syst. Rehabil. Eng. 21 567
[13] Chen H B, Feng J C, Fang Y 2008 Chin. Phys. Lett. 25 405
[14] Li Y, Wang J, Zurada J M 2000 IEEE Trans. Neural Networks 11 1413
[15] L S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506
[16] Scholkopf B 2001 Adv. Neural Inf. Proc. Syst. 13 301
[17] Kwak N 2013 IEEE Trans. Neural Networks and Learning Systems 24 2113
[18] Karaboga D, Basturk B 2007 J. Global Optim. 39 459
[19] Karaboga D, Basturk B 2008 Appl. Soft Comput. J. 8 687
[20] Chen Y, L S X, Wang M J, Feng J C 2015 Acta Phys. Sin. 64 090501 (in Chinese)[陈越, 吕善翔, 王梦蛟, 冯久超2015 64 090501]
[21] Hyvarinen A, Oja E 2000 Neural Networks 13 411
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